This project focuses on new quantitative methodologies for studying developmental pathways leading to onset of health-related outcomes over time, such as early-onset of substance involvement among youth. The project centers on the development and refinement of two sophisticated strategies for examining longitudinal mediation hypotheses: statistical mediation with discrete-time survival analytic outcomes, and statistical mediation in two-part onset-to-growth models, both of which are not yet well understood. The work involves intensive simulation studies augmented by application of the methods to an actual longitudinal data set. Making use of a 10-year longitudinal data set following a predominantly African American sample of children from age 5 to age 14 (with 92% retention), this real-data application seeks to understand the practical limitations and to refine the integrated statistical methodologies. The project has two phases. The models developed and evaluated in the first phase involve the integration of mediation with discrete-time survival analysis tested through: (a) a series of statistical simulations to evaluate empirical power, Type 1 error rates, confidence interval coverage, as well as bias and relative bias of point estimates in the model; (b) application to the real data set; and, (c) refinement of the original simulations based on information garnered from the application. The models developed and evaluated in the second phase involve the integration of mediation with two-part onset- to-growth models tested through: (a) a series of simulation studies to evaluate empirical power, Type 1 error rates, confidence interval coverage, as well as bias and relative bias of point estimates; (b) application to the real data set; and, (c) refinement of the original simulations based on information garnered from the application. The project aims to development guidelines for utility and optimum use of the new methods and to gauge the benefit of two-part onset-to-growth mediation models over discrete-time survival mediation models. The new methodologies have the potential to help strengthen future research within the substance-abuse field and in other biomedical fields. For example, these approaches can be applied to studies investigating biological/genetic markers as predictor variables that operate via neural processes (acting as mediators) to impact trajectories of substance-use onset and growth. Similarly, this type of framework can be applied to mediational models in both etiological and prevention research that pertain to school dropout, development of obesity, relationship between substance use and adverse outcomes associated with risky sexual behavior, and many other areas. PUBLIC HEALTH RELEVANCE: Sophisticated quantitative methods are needed to study the unfolding of early involvement with drugs and alcohol in late childhood and early adolescence, which is a serious public health problem. The project refines and tests state-of-the-art methods that will help scientists better understand the pathways and explanations for why and how specific environmental, personal, biological, and genetic factors affect the start and exacerbation of substance use. These same quantitative tools can be applied to other health-related problems that develop over time, such as obesity, cancer risk, sexually transmitted diseases, and problematic brain development.